Achromatic telephoto objective lens

ABSTRACT

An achromatic objective lens comprises three to five components, of which at least two are positive and at least one is negative. At least one of the positive components is formed of fluophosphate crown glass or phosphate crown glass. At least one of the other positive components is formed of barium flint glass. At least one of the negative components is formed of lanthanum glass or antimony flint glass.

7/ I" 6 Q 1 w (0A) o United State. m g 3 1 3,774,991 Shimizu Nov. 27, 1973 ACHROMATIC TELEPHOTO OBJECTIVE 2.850.945 9/1958 Kohler 350/177 LENS 3,249,009 5/1966 Lescher et al.

3,502,394 3/1970 Kobayashi 350/216 [75] Inventor: Yoshiyuki Shimizu, Kawasaki, Japan [73] Assignee: Nippon Kogaku K.K., Tokyo. EXami'lef-l0hn Corbin Japan Attorney-Joseph M. Fitzpatrick et al.

[22] Filed: Dec. 20, 1971 [57] ABSTRACT [21 Appl. No.: 209,617 I An achromatic objective lens comprlses three to five components, of which at least two are positive and at [30] Fore'gn Applicauo Priomy Data least one is negative. At least one of the positive com- Dec. 25, 1970 Ja an 45/125634 ponents is formed of fluophosphate crown glass or phosphate crown glass. At least one of the other posi- [52] 11.8. CI 350/215, 350/177, 350/220 tive components is formed of barium flint glass. At [51] Int. Cl G02b 9/34, G02b 9/62, G02b 13/02 least one of the negative components is formed of lan- [58] Field of Search 350/215, 177, 220 thanum glass or antimony flint glass.

[5 References Cited 6 Claims, 24 Drawing Figures UNITED STATES PATENTS Herzberger et a1. 350/215 dlo dn (112 PATENTEDNUV 27 I975 SHEET 10F 7 FIG.

FIG.IB FIG. IC FIG. ID

ASTIGMATISM DISTORSION SPHE I ABER a FIG. 2A

FIG 20 SINE ASTIGMATISM CONDITION FIG.2D

DISTORSION PAIENTEDnuvzv I973 SHEET U 0F 7 FIG. 4A

I? refs DISTORSION W 'y /l5.6

SPHERICAL QRE ASTIGMATISM CONDITION O fi/Alll... llllll ll 0 d 5 m PAIENIED NOV 2 7 I975 FIG.5B

SHEET 5 [IF 7 FIG. 5A

FIG.5C

dumdlz FIG. 5D

DISTORSION ACI-IROMATIC TELEPHOTO OBJECTIVE LENS BACKGROUND OF THE INVENTION 1. Field of the Invention This invention relates to an achromatic objective lens suitable for photography, or the like.

2. Description of the Prior Art If a thin composite lens system, comprising simply of two lenses joined together, is made so as to be achromatic for light having a wavelength pg for g-line of the spectrum with respect to light of a wavelength pd for d-line of the spectrum as reference wavelength (see FIG. 6), then the focal length f of the lens system for a third wavelength pc and c-line of the spectrum will be expressed as:

where f, represents the focal length for the reference wavelength d represent the refractive indices for the wavelengths pd, pg and pc, and the subscript numbers 1 and 2 relate to positive and negative lenses, respectively, Af is the socalled secondary spectrum.

The value of D may be variable depending on such factors as the glass in use and the wavelengths in use, but since in ordinary glasses the values of vg and k are substantially proportionate to each other, the numerator in equation 1 does not become zero. Thus, the equation shows that achromatism for three different wavelengths is impossible with an achromatic lens formed of two glass components.

For example, a combination of glass components which can show sufficiently difl'erent dispersive powers for d-line, g-line and c-line of the spectrum will usually provide a substantially constant value of approximately l/l ,000. Therefore, if an achromatic lens for photography is made achromatic for d-line and g-line, its focal length for c-line will be increased by about 0.1 percent, which is not a negligible value in an optical system of great focal length used for precision measurements. In order to reduce this value, it is preferable, as seen from equation 1, that the glass, for the positive component, has a smaller value of k while the glass for the negative component has a greater value of k. This will-reduce the numerator of equation 1 and decrease the value of D. Ideally, the values of k in the positive and negative lenses should be such that k, k,, which establishes achromatism for three different wavelengths.

Further, the glass for the positive component should desirably have a large valueof v,, i.e. a low dispersive power, while the glass for the negative component should have a small value of v, i.e. a high dispersive power.

This increases the denominator in equation 1 and decreases the value of D. As mentioned previously, however, in the optical glasses usually used, values of v, and k are substantially proportionate to each other and consequently, the value of D maintains a substantially constant level. Thus, it is diflicult to find a desired glass. For this reason, materials other than glasses, such as quartzite, have been used as a material for reducing the value of D. Japanese Patent publication No.

24,069/ 1969, for example, discloses a telephoto lens having a forward lens group comprising three components including a positive, a negative and a positive component, of which the negative component is formed of flint glass or barium flint glass and is interposed between the two positive components (see FIG. 7). In such a combination of components, namely, components of quartzite and flint glass or barium flint glass, the value of D is reduced to about one-third or one-fourth the value as compared with the case where only ordinary glasses are used, and thus very good correction of chromatic aberration can be expected. However, problems are encountered because quartzite is more expensive than ordinary glasses and it is difficult to machine and it is difficult to obtain in a large size.

SUMMARY OF THE PRESENT INVENTION In view of the foregoing, the present invention intends to .reduce the quantity of secondary spectrum down to a fraction of that obtained by the prior art, without using any crystalline material of low dispersive power, such as quartn'te or the like. However, optical glasses are much poorer in partial dispersion and dispersive power than crystalline materials such as quartzite and the like, and the value of D cannot be reduced as much as in the case of quartzite, even if phosphate crown glass or fluophosphate crown glass is used for the positive component and antimony flint glass is used to reduce the secondary spectrum, or lanthanum glass having similar properties is used for the negative component so as to accomplish an achromatism for two lines. In these cases, however, by adding a third positive component formed of a glass having a value of equivalent to the negative component and having a smaller absolute value of k than that of the negative component, and increasing the negative power of the negative component so as to negate the power of the additional positive component, the composite lens comprising the negative component and the thirdpositive component and having a negative focal length could be made to show very little variation in the value of v, and to show an apparent value of k nearly equivalent to that of the first positive component formed of phosphate crown glass or fluophosphoric acid crown glass, thereby reducing the apparent value of D. This means that in equation I the magnitude of the value of k is reversed between the negative component and the additional or third positive component, so that the symbol (positive or negative) of D is reversed to cause a secondary spectrum of the opposite symbol, thus resulting in an optical system having a reduced quantity of secondary spectrum.

Moreover, at the same time, the initially established achromatism for two wavelengths is maintained as it is, and when the combined value of k of the negative and the third positive component becomes equal to the value of k of the first component, there is established an achromatism for three wavelengths and further, in an extreme case, the symbol of the secondary spectrum is reversed. Generally, by using n types of different glasses to make n components and by suitably determining the powers of the respective components, it will be proved that achromatism for n difi'erent wavelengths can be established.

In an ordinary optical system, however, an achromatism for three wavelengths, effected in the vicinity of d, g and c or d, F and c would be sufficient because the other wavelengths do not have a great difference therefrom. For this purpose, at least three components formed of at least three different glasses are required.

As the result of experiments carried out on various combinations of these three different glasses, it has been found that the combination of phosphate crown glass or fluophosphate crown glass of low dispersive power for the positive components and lanthanum glass or antimony glass for the negative component of barium flint glass, may provide a good result. This is due to the fact that phosphate crown glass and fluophosphate crown glass each have a low dispersive power, that the absolute value of k of lanthanum or antimony glass used for the negative component is relatively great, and that barium flint glass has a value of v, nearly equal to that of lanthanum or antimony glass and has an absolute value of k lower than that of lanthanum or antimony glass.

The present invention is based on the concept described heretofore, and embodiments thereof shown and described hereinafter are applications of such concept to the forward lens group of a telephoto lens which is useful as a long-focus lens for photography.

The optical system of the present invention constitutes an objective lens whose forward lens group comprises three to five components, of which at least two are convergent and at least one is divergent. At least one of these components is a positive one formed of phosphate crown glass or fluophosphate crown glass, at least one of them is a positive component formed of barium flint glass, and at least one of them is a negative component formed of lanthanum glass or antimony flint glass. Thus, correction of chromatic aberration is achieved in the forward lens group.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. IA is a longitudinal sectional view of an optical system formed according to the present invention;

FIG. 1B is a graphical illustration of the spherical aberration of the optical system of FIG. 1A;

FIG 1C is a graphical illustration of the astigmatism of the optical system of FIG. 1A;

FIG. 1D is a graphical illustration of the distortional aberration of the optical system of FIG. 1A;

FIG. 2A is a longitudinal sectional view of an optical system formed according to a second embodiment of the present invention;

FIG. 2B is a graphical illustration of the spherical aberration of the optical system of FIG. 2A;

FIG. 2C is a graphical illustration of the astigmatism of the optical system of FIG. 2A;

FIG. 2D is a graphical illustration of the distortional aberration of the optical system of FIG. 2A;

FIG. 3A is a longitudinal sectional view of an optical system formed according to a third embodiment of the present invention;

FIG. 3B is a graphical illustration of the spherical aberration of the optical system of FIG. 3A;

FIG. 3C is a graphical illustration of the astigmatism of the optical system of FIG. 3A;

FIG. 30 is a graphical illustration of the distortional aberration of the optical system of FIG. 3A;

FIG. 4A is a longitudinal sectional view of an optical system formed according to a fourth embodiment of the present invention;

FIG. 4B is a graphical illustration of the spherical aberration of the optical system of FIG. 4A;

FIG. 4C is a graphical illustration of the astigmatism of the optical system of FIG. 4A;

FIG. 4D is a graphical illustration of the distortional aberration of the optical system of FIG. 4A;

FIG. 5A is a longitudinal sectional view of an optical system formed according to a fifth embodiment of the present invention;

FIG. 5B is a graphical illustration of the spherical ab erration of the optical system of FIG. 5A;

FIG. 5C is a graphical illustration of the astigmatism of the optical system of FIG. 5A;

FIG. 5D is a graphical illustration of the distortional aberration of the optical system of FIG. 5A;

FIG. 6 is a graph illustrating the mode of achromatism in achromatic lens for two wavelengths of focal length f mm using two types of conventional glasses;

FIG. 7 is a graph illustrating the mode of achromatism at the axial image point when the focal length of the conventional telephoto lens using two components formed of quartzite is converted to f I00 mm;

FIG. 8 is a graph illustrating the mode of achromatism at the axial image point when the focal length of the lens system of Example II of the present invention is converted to f I00 mm; and

FIG. 9 is a graph illustrating the mode of achromatism at the axial image point when the focal length of the lens system of Example V of the present invention is converted to f= 100 mm.

DESCRIPTION OF THE PREFERRED EMBODIMENTS Referring to FIGS. 1A, 2A, 3A, 4A and 5A, there are shown, in longitudinal section, five examples of the optical system according to the present invention. As shown, the optical system constitutes an objective lens having a forward lens group, which comprises at least two convergent components and at least one divergent component. The total number of components in the forward lens group may range from three to five. In FIG. IA (Example I), the forward lens group comprises four components, of which three are convergent and one is divergent. In FIGS. 2A, 3A and 4A (Examples II, III and IV), two convergent components and one divergent component are used. In FIG. 5A (Example V), three convergent components and two divergent components are used. In all of these various examples, at least one component in the forward lens group is a positive component formed of phosphate crown glass or fluophosphate crown glass, at least one component is a positive component formed of barium flint glass, and at least one component is a negative one formed of Ianthanum glass or antimony flint glass.

Various data of the respective examples are shown in the tables below, where r represents the radius of curvature of each component, d the center thickness of air gap of each component, n the refractive index of each optical glass in use, and v the Abbe number of each optical glass.

Various aberrations in Examples I to V are shown in FIGS. lB,-C, D to 58, C, D, where the curve m represents the astigmatism for meridional rays and the curve s represents the astigmatism for spherical rays.

The modes of achromatism of the axial image points in Examples II and V, when the focal length is converted to f= 100 mm, are illustrated in FIGS. 8 and 9, respectively. 4

Example 1 r +430.0 d 7.0 n,, =1 .62374 Focal length f 300.0; Relative aperture F/4.5; v =47.0 Angle of field 8.4" r, 449.9 r +106.0 d, 11.0 n =l.48606 Example V v =8l.5 (Fluophosphoric acid glass) 5 Focal length f 1,200; Relative aperture PH 1; r, 151.0 d, 4.0 Angle of field 4 r;,=l44.0 d 3.0 n,,=1.744 r, =+310.0 d, 11.0 n,, =l.61405 v =44.9 (lanthanum glass) v,,=55.1(bibarium flint glass r +130.0 d 12.0 n,,=1.6393 r 525.0 d, 5.0 v =45.0 (barium flint glass) r --630.0 (1,, 7.5 n =1.6115 r, 650.0 d, 1.0 v =44.3(antimony flint glass r =+95.0 d 7.7 n =1.48606 r =+3l3.0 d =4.0 r =+341.3 d,,= 10.0 n v =8l.5 (fluophosphoric acid glass) =1 .48606 r +878.8 d, =119.3 v =8 l .5(fluophosphoric acid glass r 43.0 d 1.0 n =1.62041 l5 r 557.0 d 7.0 v =60.3 r 4l3.0 d 7.5 n =1 .713 r, +l50.0 d, 3.5 n =l.62004 1 53.9(lanthanum glass) v =36.3 r +8 14.0 d; 1.0 r 104.82 r +7000 :1, 10.0 n, =1.62374 Example 11 v,;=47.0(barium flint glass) Focal length f 600.0; Relative aperture f/5.6; r =-2386.1 d =533.0 Angle of field 8 r 190.0 d 2.0 n =l.5168 r +200.000 d 15.0 11,, =l.48606 v,,=64.2

l -=8 1 .5 (fluophosphoric acid glass) r +310.0 d 7.0 n,, =1 .62374 r, 277.348 d, 6.0 v,,=47.0 r, 277.348 d, 6.0 Il =1.744 r 472.83

v =44.9 (lanthanum glass) Although the invention has been shown and der +387.299 d 1.5 scribed as applied to a telephoto lens, it is to be underr, +244.820 d, 10.0 '1 =1.56965 stood that the present invention may also be applicable v =49.5 (ban'um flint glass) to the objective lens in a telescope, microscope, etc. r, +4430.700 d,=254.0 1 claim: r 93.000 d, 1.5 n,, =1 .52682 1. In a telephoto lens system including a forward achv =5 1.1 romatic objective lens group and a rear group, said forr, 180.000 d 6.0 n,, =l.62374 ward group comprising at least three components of v =47.0 which at least two are convergent and at least one is dir 148.925 vergent, at least one of said convergent components Example 111 being formed of glass selected from the group consist- Focal length f 800.0; Relative aperture F/8; Angle of field 6.

ing of fluophosphoric acid glass and phosphoric acid glass, at least one of the other convergent components r +300.0 d 13.0 n =l.48614 40 being formed of barium flint glass, said divergent comv =81.5(fluophosphoric acid glass) ponent being formed of glass selected from the group r, 430.0 d, 7.3 consisting of lanthanum glass and antimony flint glass, r, =382.5 d, 7.5 n, =1.61266 said rear group being spaced a substantial distance v, =44.3(antimony flint glass) from said forward group. r +310.0 d 1.5 2. An achromatic objective lens as defined in claim r, +292.0 d 10.0 n, =1 .56953 1, wherein said components have the following characv,;=49.5(barium.flint glass) teristics; r, 1654.4 d #350 Focal length f=300.0; Relative aperture F/4.5', r, 150.0 d, 2.0 n =1.5l885 Angle of field 8.4

v =59.0 r 106.0 d =11.0 n =1.48606 r, d 5.0 n,, =l.62399 8 1 .5 fluophosphoric acid glass v =47.0 r 151.0 d, 4.0 r, 233.27 r 144.0 d, 3.0 n =1.744 Example 1V v =44.9 lanthanum glass Focal length f 1,200 Relative aperture Fl] 1; r 130.0 :1. =12.0 n =l.6393 Angle of field 4 P545 .0 barium flint glass r +403.0 d,= 13.0 n, =1 .48606 r 650.0 d,, 1.0

v =81.5(Fluorophosphoric acid glass) r, 95.0 d, 7.7 n =1.48606 r, 413.0 d 8.0 v =81.5 fluophosphoric acid glass r, 428.0 d, 6.0 n,, =1.744 r, 878.8 d, =119.3

v =44.9(1anthanum glass) r 43.0 d, 1.0 n =l.6204l r. =+1 168.1 d 2.0 v,,=60.3 r, +550.0 d,'- 10.0 n =1.56965 r, =1- l50.0 d 3.5 n,, =1 .62004 v =49.5(barium flint glass) v ==36.3 r10 r-, =190.0 d 2.0 n, =1.5168 wherein r represents the radius of curvature of each v,,=64.2 component,

d the center thickness or air gap of each component, n the refractive index of each glass for Helium dline of spectrum, and

y the Abbes number of each glass for Helium d-line of spectrum.

3. An achromatic objective lens as defined in claim 1, wherein said components have the following characteristics:

focal length f=600.0; Relative aperture Fl5.6 Angle of field 8.

r 200.000 d 15.0 rip-1.48606 v =8l.5 fluophosphoric acid glass r, 277.348 d 6.0 n =1.744

v =44.9 lanthanum glass r 224.820 d, 10.0 n,,=1.56965 v =49.5 barium flint glass r 93.000 d, 1.5 n,,=1.52682 r, 180.000 d 6.0 n =1.62374 wherein r represents the radius of curvature of each component,

d the center thickness or air gap of each component, n, the refractive index of each glass for Helium d-line of spectrum, and

11,, the Abbes number of each glass for Helium d-line of spectrum.

4. An achromatic objective lens as defined in claim 1, wherein said components have the following characteristics:

Focal length f=800.0; Relative aperture F/8; Angle of field 6 r 300.0 d,= 13.0 n,,=1.48614 v =8l.5 fluophosphoric acid glass r 382.5 d; 7.5 n =1.61266 v,,=44.3 antimony flint glass r, 292.0 d, =10.0 n,,=1.56953 v =49.5 barium flint glass r-, 150.0 d, 2.0 n =1.51885 wherein r represents the radius of curvature of each component,

d the center thickness or air gap of each component, n the refractive index of each glass for Helium d-line of spectrum, and v, the Abbes number of each glass for Helium d-line of spectrum.

5. An achromatic objective lens asdefined in claim 1, wherein said components have the following characteristics:

focal length f=1,200; Relative aperture F/l 1; Angle of field 4 r 403.0 d, 13.0 n,, =1.48606 v =81.5 Fluophosphoric acid glass r 428.0 d; 6.0 n, =1.744

v,,=44.9 lanthanum glass r, 550.0 d 10.0 m, =l.56965 v =49.5 barium flint glass r, 190.0 d, 2.0 n,, =l.5168

r =1- 430.0 d,, 7.0 n,, =1 .62374 wherein r represents the radius of curvature of each component,

d the center thickness or air gap of each component, n the refractive index of each glass for Helium d-line of spectrum, and

11,, the Abbes number of each glass for Helium d-line of spectrum.

6. An achromatic objective lens as defined in claim 1, wherein said components have the following characteristics:

Focal length F1200; Relative aperture F/l 1;

wherein r represents the radius of curvature of each component, d the center thickness or air gap of each components,

, n the refractive index of each glass for Helium d-line of spectrum, and v the Abbes number of each glass for Helium d-line of spectrum.

1: w a: a 4

UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent N... 5,774,991 November 27, 1973 Inventofls) YOSHIYUKI SHIMIZU It is certified that error appears in the above-identified patent and that said Letters Patent are hereby correctedas shown below:

Column 1, line 14, change "11 and c-line" to 1c for c1ine -:;11

line 16, change "Af f f [(k f (g1 zy f Df w Af f f [(k1- 2)/ "g2')] d Column 2, line 33, change "value of-u to value of v Column 5, between lines 6 and 7, bene th r and above r insert d line 29, change "r =+244.820" to i r =+224.j820 line 58, change "(F1uorophosphoric" to (Fluophosphoric n V Column 6, line 12 delete "r 341. 3 d =f 10.0 n3"; 1 I

- 1 line 13. before "=1.48606", insert r 341.3 d5= 10.0 1 n Signedand sealed this 30th day of July 1974.

(SEAL) Attestz v McCOY M. GIBSON, JR. C. MARSHALL DANN Attesting Officer Commissioner of Patents Q P040 0769, USCOMM-DC opus-Pee Q 7 i ".5. GOVERNMENT PRINTING OFFICE: I), 0-1.51". 

2. An achromatic objective lens as defined in claim 1, wherein said components have the following characteristics; Focal length f 300.0; Relative aperture F/4.5; Angle of field 8.4* r1 + 106.0 d1 11.0 nd 1.48606 Nu d 81.5 fluophosphoric acid glass r2 - 151.0 d2 4.0 r3 - 144.0 d3 3.0 nd 1.744 Nu d 44.9 lanthanum glass r4 + 130.0 d4 12.0 nd 1.6393 Nu d 45.0 barium flint glass r5 + 650.0 d5 1.0 r6 + 95.0 d6 7.7 nd 1.48606 Nu d 81.5 fluophosphoric acid glass r7 + 878.8 d7 119.3 r8 - 43.0 d8 1.0 nd 1.62041 Nu d 60.3 r9 + 150.0 d9 3.5 nd 1.62004 Nu d 36.3 r10 - 104.82 wherein r represents the radius of curvature of each component, d the center thickness or air gap of each component, nd the refractive index of each glass for Helium d-line of spectrum, and Nu d the Abbe''s number of each glass for Helium d-line of spectrum.
 3. An achromatic objective lens as defined in claim 1, wherein said components have the following characteristics: focal length f 600.0; Relative aperture F/5.6 Angle of field 8*. r1 + 200.000 d1 15.0 nd 1.48606 Nu d 81.5 fluophosphoric acid glass r2 - 277.348 d2 6.0 r3 - 277.348 d3 6.0 nd 1.744 Nu d 44.9 lanthanum glass r4 + 387.299 d4 1.5 r5 + 224.820 d5 10.0 nd 1.56965 Nu d 49.5 barium flint glass r6 + 4430.700 d6 254.0 r7 - 93.000 d7 1.5 nd 1.52682 Nu d 51.1 r8 + 180.000 d8 6.0 nd 1.62374 Nu d 47.0 r9 - 148.925 wherein r represents the radius of curvature of each component, d the center thickness or air gap of each component, nd the refractive index of each glass for Helium d-line of spectrum, and Nu d the Abbe''s number of each glass for Helium d-line of spectrum.
 4. An achromatic objective lens as defined in claim 1, wherein said components have the following characteristics: Focal length f 800.0; Relative aperture F/8; Angle of field 6* r1 + 300.0 d1 13.0 nd 1.48614 Nu d 81.5 fluophosphoric acid glass r2 - 430.0 d2 7.3 r3 - 382.5 d3 7.5 nd 1.61266 Nu d 44.3 antimony flint glass r4 + 310.0 d4 1.5 r5 + 292.0 d5 10.0 nd 1.56953 Nu d 49.5 barium flint glass r6 - 1654.4 d6 435.0 r7 - 150.0 d7 2.0 nd 1.51885 Nu d 59.0 r8 Infinity d8 5.0 nd 1.62399 Nu d 47.0 r9 - 233.27 wherein r represents the radius of curvature of each component, d the center thickness or air gap of each component, nd the refractive index of each glass for Helium d-line of spectrum, and Nu d the Abbe''s number of each glass for Helium d-line of spectrum.
 5. An achromatic objective lens as defined in claim 1, wherein said components have the following characteristics: focal length f 1,200; Relative aperture F/11; Angle of field 4* r1 + 403.0 d1 13.0 nd 1.48606 Nu d 81.5 Fluophosphoric acid glass r2 - 413.0 d2 8.0 r3 - 428.0 d3 6.0 nd 1.744 Nu d 44.9 lanthanum glass r4 +1168.1 d4 2.0 r5 + 550.0 d5 10.0 nd 1.56965 Nu d 49.5 barium flint glass r6 -6230.7 d6 575.0 r7 - 190.0 d7 2.0 nd 1.5168 Nu d 64.2 r8 + 430.0 d8 7.0 nd 1.62374 Nu d 47.0 r9 -449.9 wherein r represents the radius of curvature of each component, d the center thickness or air gap of each component, nd the refractive index of each glass for Helium d-line of spectrum, and Nu d the Abbe''s number of each glass for Helium d-line of spectrum.
 6. An achromatic objective lens as defined in claim 1, wherein said components have the following characteristics: Focal length f 1,200; Relative aperture F/11; Angle of field 4*. r1 + 310.0 d1 11.0 nd 1.61405 Nu d 55.1 bibarium flint glass r2 - 525.0 d2 5.0 r3 - 630.0 d3 7.5 nd 1.6115 Nu d 44.3 antimony flint glass r4 + 313.0 d4 4.0 r5 + 341.3 d5 10.0 nd 1.48606 Nu d 81.5 fluophosphoric acid glass r6 - 557.0 d6 7.0 r7 - 413.0 d7 7.5 nd 1.713 Nu d 53.9 lanthanum glass r8 + 814.0 d8 1.0 r9 + 700.0 d9 10.0 nd 1.62374 Nu d 47.0 barium flint glass r10 -2386.1 d10 533.0 r11 - 190.0 d11 2.0 nd 1.5168 Nu d 64.2 r12 + 310.0 d12 7.0 nd 1.62374 Nu d 47.0 r13 - 472.83 wherein r represents the radius of curvature of each component, d the center thickness or air gap of each components, nd the refractive index of each glass for Helium d-line of spectrum, and Nu d the Abbe''s number of each glass for Helium d-line of spectrum. 